An important aspect of cost-effectively executing a Fleet Management Program (hereinafter “FMP”) is determining maintenance schedules (MS) that minimize maintenance costs such as the cost of maintenance work and of parts of an engine over a longer time interval. Maintenance schedules depend upon a number of parameters such as maintenance time intervals, thresholds for changing or upgrading engine components, etc. The challenge lies in determining which parameter values minimize the resultant maintenance costs of an engine during an interval of the lifetime of the engine.
This determination is generally characterized as a multi-objective global optimization problem, where the objectives are the mentioned costs. For improved cost predictions it may be useful to take into account not only the current state of an engine to be serviced but to consider also an estimated cost incurred at future shop visits during the lifetime of the engine. Moreover, the cost predictions may be further improved by taking into account future probabilities of failure during the service life of the engine. These aspects are usually handled by simulations of the service life of the engine taking into account stochastic events. Thus, the multi objective global optimization problem of optimizing a maintenance schedule has in addition both a time dependent characteristic and a stochastic characteristic. Moreover, a maintenance schedule by itself may be a quite complex and long running program that considers different combinations of parts to be replaced and different types of work that may be implemented and that takes into account the usage of the parts and other aspects of maintenance to propose a current best set of maintenance decisions. Such maintenance decisions may include what parts have to be replaced and what maintenance work has to be performed. The optimization problem is nonlinear and has constraints.
Generally, the multi-objective global optimization problem is a mixed integer problem since some optimization parameters may be integer variables, such as decisions to be taken or not taken, or continuous variables such as time limits. All these aspects of the multi-objective global optimization problem usually make the optimization problem hard to solve. Difficulties with classical optimization approaches when facing such problems are known to one of ordinary skill in the art. For example, classical exhaustive optimization techniques can provide high confidence that the best solutions are found, such as by enumerations; grid searches, or graph searches; however, these techniques require too large computational time especially when considering a larger number of parameters. In contrast, branch and bound techniques are known to have difficulties handling multiple objectives. Stochastic approaches, such as evolutionary algorithms, simulated annealing, genetic algorithms, tend to find local optima and may provide limited confidence that global optima are found, while gradient based or pattern search approaches tend to find a local optimum, etc.
Therefore, for the optimization of maintenance schedules of aircraft engines, there exists a need for a multi objective optimization procedure that takes into account the time dependent and stochastic nature of the problem and that is designed to overcome the above mentioned difficulties.